CAT 2022 Slot 1 QA Q15 Equations

Question 15 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

Let \(a\) and \(b\) be natural numbers. If \(a^2+a b+a=14\) and \(b^2+a b+b=28\), then \((2 a+b)\) equals
  1. A
    7
  2. B
    10
  3. C
    9
  4. D
    8

Answer: (D) 8 Equations MCQ

Solution

  1. Factor: \(a(a + b + 1) = 14\) and \(b(a + b + 1) = 28\).
  2. Adding: \((a + b)(a + b + 1) = 42 = 6 \times 7\), so \(a + b = 6\).
  3. Then \(a = \frac{14}{7} = 2\), \(b = \frac{28}{7} = 4\), and \(2a + b = 8\).

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